Find the polynomial in X where zeros are -2, -1 and 3.
Please someone help me with this. Thanks
x= -2 , x= -1, x= 3
= (x 2)(x 1)(x-3)
then you factorise
(x�0…5 3x 2)(x-3)
x(x�0…5 3x 2) - 3(x�0…5 3x 2).
Hope you can go on from here.
polynomial is (x+2)(x+1)(x-3)
or
(x+2)(x^2 - 2x - 3)
= x^3 - 2x^2 - 3x + 2x^2 - 4x - 6
= x^3 - 7x - 6
To find the polynomial when the zeros are given, you can use the factored form of the polynomial. The factored form of a polynomial with zeros -2, -1, and 3 can be written as follows:
(x - (-2))(x - (-1))(x - 3)
Simplifying this expression, we get:
(x + 2)(x + 1)(x - 3)
To find the polynomial, we expand the expression:
(x + 2)(x + 1)(x - 3) = (x^2 + 3x + 2x + 6)(x - 3)
= (x^2 + 5x + 6)(x - 3)
= x^3 + 5x^2 + 6x - 3x^2 - 15x - 18
= x^3 + 2x^2 - 9x - 18
Therefore, the polynomial with zeros -2, -1, and 3 is x^3 + 2x^2 - 9x - 18.